All mice are not created equal and mouse support varies. My Microsoft mouse has a tilting scroll wheel and five programable buttons. It would be easy to program the "[" and "]" keys to change brush size to mouse buttons. LR is not needed so I do not install it so I do not know how LR scrolls brush size.
Ashvin, I have a Mac with wacom tablet. Have you tried holding down the Control + left click and drag left and right for cursor size and Control +left click and drag up and down for hardness. You must have a painting or selection tool selected for this to work. Once you are used to this method, it is very fast.